A183074 Prime numbers p such that 2^p - 1 is composite and each of its prime divisors has the form 4j + 3.

43, 79, 193, 311, 331, 349, 389, 557, 577, 631, 647, 1103

Offset: 1

Author

Stuart Clary, Dec 23 2010

Keywords

• nonn
• hard

Comments

Needed factorizations are in the Cunningham Project.

Examples

			43 is in this sequence because 2^43 - 1 = 431 * 9719 * 2099863, and each of those primes has the form 4j + 3.
		

Links

• S. S. Wagstaff, Jr., The Cunningham Project.

Crossrefs

Cf. A000043, A136003, A183071, A183072, A183073.

Cf. A000668, A136005, A183075, A183076, A183077, A183078.

Programs

Mathematica

cQ[n_]:=Module[{x=2^n-1},!PrimeQ[x]&&Union[Mod[Transpose[ FactorInteger[ x]][[1]],4]]=={3}]; Select[Prime[Range[120]],cQ] (* Harvey P. Dale, Jun 17 2014 *)

Formula

A183078(n) = 2^a(n) - 1.

Extensions

a(12) from Amiram Eldar, Feb 18 2019